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Subject: аннотация к книге topol. According to the A. Teleiko, M. Zarichnyi in their book Categoricacal Topology of Compact Hausdorff Spaces discusses different constructions of general and algebraic topology, demonstrating their categorical nature. It describes, in particular, on classical structures hyperspace or space of probability measures.The authors note that the basic theory of standard functors in the category of compact Hausdorff spaces have been laid by Evgenii Shchepin. The foundation of theory of normal functor in the category of compact Hausdorff spaces has been laid by Evgenii Shchepin. A. Teleiko, M. Zarichnyi goes on to say: the notion of normal functors turned out to be sufficiently wide to contain many interesting functors and, at the same time, sufficiently special for developing a meaningful theory. Different properties of functors close to being normal were investigated by V. Fedorchuk, A. Dranishnikov, A. Chigogidze, A. Ivanov, M. Smurov, V. Basmanov, E. Moiseev, A. Savchenko, T. Banakh, T. Radul, O. Nykyforchyn, and other authors. The book is organized as follows. In the first chapter the authors describe the information about general topology and category theory. In fact provides information on Shchepin spectral theorem, dimension, Milutin maps, monads, Eilenberg-Moore category of a monad, Kleisli categories, extensions of contravariant functors. Second chapter of this book the authors devote the general theory of functors in the category of compact Hausdorff spaces and relate categories are concentrating around the notion of normal functor. One of the important general problems consider in this chapter is the problem of intrinsic characterization of concrete functors or classes of functors. Chapter 3 deals with monads generated by functors close to being normal. In particular, A. Teleiko, M. Zarichnyi considers here the problem of characterization of the categories of algebras, extension of functor onto the categories of algebras. For example, the Kleisli categories naturally appear in the topology in the context of multivalued maps. In Chapter 4 the authors gives information about some application of functor and monads to geometric topology. In other words: preservation of finite-dimensional manifolds, preservation of ANR-spaces and manifolds, preservation of -spaces, functors and G-ANR-spaces, shape and homotopy properties of functors. In addition theorem 4.2.3 is proved by V. Basmanov (1983). The authors note that the second part of the proof (reduction of general case to the case of finite-dimensional spaces) literally follows the arguments by V. Fedorchuk. The Basmanov theorem generalizes the series of results in this direction. In Chapter 5 the authors provide results to general topology of compact nonmetrizable spaces. The exposition in these chapters is necessarily far from being self-contained; the primary objective is give diverse examples of connections between the theory developed in Chapter 2, 3 and topology of absolute extensors, (infinite-dimensional) manifolds, equivariant topology. Moreover the metod of characteristics in investigations of uncountable functors-powers (theorem 5.1.4) is invented by E. Shchepin. Theorem 5.1.30 is proved by A. Smurov. Theorem 5.2.3 is proved by A. Ivanov. The examples of this Section are constructed by M. Zarichnyi. Also A. Teleiko, M. Zarichnyi emphasize the fundamental contribution of E. Schepina, which laid the foundation for the theory of topological functors. |
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describe the information about... - как-то не звучит In the first chapter - С артиклями проблема у Вас... Буду читать дальше... :) |
| I would say Chapter 2 is devoted tooooo - |
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consider The authors
The book is organized as follows. |
| А вообще, ММарта, хорошо бы вам разбить свой пассаж на сегменты и предоставить оригинал с каждым (рус-англ). Слишком уж сырой перевод для простой вычитки/корректуры. |
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Абсолютно согласна со Следопытом: вижу гору и хочется не взбираться на нее, а обойти. Дайте нам несколько невысоких "горок" (с оригиналом, конечно). : ) |
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большое спасибо)) будет сделано |
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